In recent years, numerical simulations have been used widely for investigation of mechanical rock cutting. However, the capability of the modelling methods has yet remained open for question. In an attempt to address the shortcomings of the existing methods, this paper proposes a new extension of combined finite/discrete element method (FEM/DEM), which takes into account the mix-mode I-II fracture criteria for predicting the initiation and propagation of cracks. The code’s ability in modelling rock fracture process is investigated by simulating fragmentation with a mechanical cutter. The model characterized the rock-tool interaction, computing the direction of crack growth leading to chip generation. The obtained results demonstrated the capability of the proposed combined FEM/DEM method in modelling mechanical rock cutting process. The code could successfully handle the chipping process, being able to model the stress concentration, crack initiation, crack propagation and chip separation.

1. INTRODUCTION

During the past decades the application of mechanical tools for rock fragmentation has been extended widely in mining and civil engineering industries; providing a more flexible and environmentally friendly alternative to conventional blasting method. However, the rock fragmentation mechanism with a mechanical cutter has not well understood due to the complexity of the dynamic interaction between mechanical tool and rock, and rock fracture process (Ghamgosar and Erarslan, 2015). While rock cutting experiments are largely used to investigate the cutting process and the associated cutting forces, the extensive number of variables and effective factors influencing the process have made the application of these tests relatively limited. The developed analytical and empirical methods also suffer from same drawback. The recent advancements in numerical modelling methods have confirmed to provide robust tools for simulation of complex problems. Hence, different numerical techniques have been considered for investigation of rock fracture process. The rock cutting process comprises of four stages that should be addressed in a numerical simulation; 1) generation of crushed zone under the tool, 2) cracks initiation and propagation from crushed zone, 3) cracks coalescence and chipping process 4) chip separation. Not all of the numerical techniques are able to model the entire rock cutting process.

One of the main challenges in seismic imaging and inversion is to build a sufficiently accurate background velocity models in the presence of complex geology. Although ray-based postmigration reflection tomography has been widely used as a workhorse for seismic depth imaging, it has some well-known and unfavorable features such as slow convergence. To avoid the dependence on the static depth errors of the reflectors on the common-image gathers, we propose an angle-domain double-difference reflection tomography approach aiming at minimizing the relative depth errors between pairs of adjacent incident angles. Condition number analysis and numerical examples demonstrate that the proposed tomographic inversion can stablely and efficiently converge toward the accurate migration velocity model.

In this paper, we proposed a novel staggered-grid low-rank finite-difference (SGLFD) scheme to solve decoupled second-order elastic wave equation. The scheme successively employs backward and forward first-order mixed-domain symbols on a staggered grid to obtain the wave extrapolation operator for second-order decoupled elastic wave propagation. The mixed-domain symbol incorporates the accurate spectral evaluation of spatial derivatives and the time-marching adjustment to ensure that the solution is exact for homogeneous wave propagation for time steps of arbitrarily large size. Considering its straightforward implementation in heterogeneous media, it's necessary to do N times inverse fast Fourier transform (FFT) every time step, where N is the total size of the model grids. In order to reduce computational cost, we apply low-rank finite difference to approximate the symbol without any FFT involved. The 2D numerical experiments demonstrate that our SGLFD method has improved the accuracy of modeling results compared with the ordinary staggered-grid finite difference method (SGFD).

This paper has been withdrawn from the Technical Program and will not be presented at the 87th SEG Annual Meeting.

In the past 30 years, the development of Computational Geophysics in China can be divided into four periods. From 1986 to 1991, it was the period of theoretical study and numerical experiment, which concentrated on the theory of tomography, inversion and pseudo-differential operator; It was the mainframe and personal computer (PC) that got widely used. From 1992 to 1997, it was the period of three dimensional (3D) imaging with integration and two dimensional imaging with wave equations, mainly studying the prestack migration, joint inversion of logging and seismic data and multi-wave data processing; We apply the high-performance PC, MIPS and SUN work station to the computation. From 1998 to 2007, it was the period of 3D imaging with wave equations, focusing on 3D wave equation prestack depth migration and 3D integration depth migration; PC-Cluster was the main tool for computation. From 2008 to now, it has been the time for 3D large-scale imaging. We do research on 3D prestack time migration, 3D reverse-time migration (RTM), 3D anisotropic RTM, 3D full wave inversion (FWI), 3D elastic RTM, and 3D elastic FWI, and adopt GPU and multinuclear CPU for computation.

Ultra-high toughness cementitious composite (UHTCC) shows prominent tensile strain-hardening and multiple-cracking characteristics, can serve as a new type of high performance material used for structure retrofitting and strengthening. The bond between corroded reinforcement and UHTCC has an apparent influence on the mechanical properties of retrofitted structural members. This paper presents an experimental investigation on the bond behavior of corroded rebar and UHTCC through central pullout tests. The experimental results revealed that for rebar with the corrosion ratio in the range of about 10%, the bond strength almost remain identical to that of original rebar whereas about 22% drop was shown for rebar with corrosion ratio of about 14%. At corrosion ratio around 10%, reinforcement with 3d bond length showed 1.5 times bond strength of that with 7d bond length. In addition with the increase in corrosion ratio, the rebar showed relatively high residual bond stress and relatively plump descending branch of bond-slip curve. Furthermore, in comparison with concrete companion samples failing in splitting, all the UHTCC samples failed in pullout due to the fine ductility of UHTCC. Based on experimental results, an empirical model of bond strength between UHTCC and corroded rebar is proposed.

In this paper, a new implicit staggered-grid finite-difference (ISFD) method is proposed with optimal difference coefficients, which is based on the sampling approximation (SA) to improve the numerical solution precision for elastic wave modeling. With the direct SA method and the plane wave theory, we derive the optimal ISFD coefficients of arbitrary even-order accuracy for the first-order spatial derivatives. We also apply these new SA-based ISFD coefficients to the solution of the first-order spatial derivatives. Through the numerical dispersion analysis of the ISFD schemes based on SA and the conventional Taylor-series expansion (TE) method, we find that this new SA-based ISFD method achieves great accuracy over a wider range of wavenumbers. The results of numerical modeling also demonstrate that the optimal method suppresses dispersion effectively, and achieves higher accuracy compared with the TE-based ISFD method.

Introduction

Numerical modeling is significant in helping understand the seismic wave propagation in complex geological models, and it also provides theory and operation supports in the process of the seismic data acquisition, processing and interpretation. Because of the ease and flexibility, the finite-difference (FD) method is very popular in numerical modeling, especially staggered-grid FD method for its competitive accuracy and stability (Dong et al., 2000; Yang et al., 2014). At the same time, for the FD method, its numerical accuracy and efficiency are greatly dependent on the schemes used for calculating spatial derivatives (Kosloff et al., 2010), and the two main schemes are explicit and implicit schemes, respectively. Although some explicit schemes often feature the simple structures and relatively small computational cost, the implicit schemes lead to greater numerical modeling accuracy and better stability.

Zhang et al. (2007) presented implicit splitting FD schemes to solve the second-order spatial derivatives in all directions. Zhou and Zhang (2011) put forward a group of optimal implicit FD schemes for the solution of the secondorder spatial derivatives with FD coefficients calculated by Fourier analysis and the least-squares. Chu and Stoffa (2012) proposed an implicit scheme in space and time domain for the scalar wave equation, showing that the implicit scheme significantly improved the precision compared with the explicit FD schemes. However, the implicit FD methods described above are only applied in acoustic wave modeling, and are difficult to extend to the solution of the first-order spatial derivatives for elastic wave equations on staggered-grid. Liu and Sen (2009) derived the implicit staggered-grid FD schemes with evenorder accuracy for the first-order spatial derivatives and implemented elastic numerical modeling. However, the ISFD coefficients are computed by the TE method, which just has great accuracy over a small frequency or wavenumber range.

This paper firstly illustrates the limitation of frequencyspace domain finite-difference forward modeling algorithm based on the rotated coordinate system which can only be applied to the equal horizontal and vertical spatial sampling interval. Then we develop a new kind of 25-point scheme based on an average-derivative optimal method (ADM). This scheme represents the approximations of the spatial derivatives as the weighted average of 5 grid points in the orthogonal directions and can be applied to different ratio of horizontal and vertical sampling interval. Therefore this scheme can be used as a general fourth-order scheme, so this method possesses excellent applicability. By determining the weighting coefficients of spatial derivative terms and the acceleration terms to minimize numerical dispersion, the number of grid points per wavelength bounded by phase velocity error range of 1% is only 2.78. We apply perfectly matched layer (PML) absorbing boundary condition to eliminate the artificial boundary reflection efficiently. The numerical examples prove the validity and precision of the ADM 25-point scheme.

Introduction

Frequency-space domain modeling is the foundation of Full waveform inversion (FWI) (Virieux and Operto, 2009). It is first fulfilled by finite element method (Lysmer and Drake, 1972), afterwards by finite difference method (Pratt, 1990). The advantage of frequency-space domain finite difference modeling (FDFDM) is that several frequency can be modeled respectively. So this method is suitable for simultaneous multi-shot modeling and avoid accumulated error.Bounded by phase velocity error range of 1%, the conventional five-point scheme proposed by Pratt(1990) needs 13 grid points per wavelength to simulate accurately. Jo et al.(1996) reduce this number to 4 based on a rotated coordinate system. But the limitation of rotated coordinate scheme is that this scheme can be only used for the circumstance of equal directional sampling intervals. Chen(2012) propsed a second-order frequencyspace domain finite-difference ADM 9-point scheme. This new scheme can not only be used for equal and uneqal directional sampling intervals, but also retain high precision.

This paper proposed a new kind of qP wave equation second-order 9-point scheme of 2D VTI media based on an average-derivative optimal method (simplified by ADM). This scheme represents the approximations of the centered spatial derivatives of 2D VTI media qP wave equation as the weighted average of 3 grid points in the orthogonal directions.Determining the optimal weighting coefficients of the second-order centered spatial derivative terms and the acceleration terms by using least-square optimal method to minimize numerical dispersion, the number of grid points per wavelength bounded by the error range of 1% is only 3.57. But the VTI conventional 9-point scheme needs approximately 12 grid points per wavelength bounded by the same error range of 1%, so the ADM method significantly increase the computational accuracy. The numerical example of complex BP2007 2D VTI ocean standard model also proves the validity and precision of the VTI media ADM 9-point scheme.

Introduction

Seismic anisotropy exists extensively all around the world (Tsvankin et al., 2010). Whereas TI media is the most common anisotropic media (Thomsen, 1986). Based on Thomsen’s famous weak anisotropy theory, Tsvankin(1996) derived P-SV wave VTI media phase velocity dispersion equation. This equation is the starting point of many researcher’s work about TI media modeling, imaging and inversion.

VTI media modeling can proceed in time-space domain or frequency-space domain. The advantage of frequency-space domain finite difference modeling (FDFDM) is that several frequency can be modeled respectively. So this method is suitable for simultaneous multi-shot modeling and avoid accumulated error. There have been some important research achievement about VTI media FDFDM. Grini et al.(2007) and Operto et al.(2007, 2009) researched mixed-grid FDFDM of viscoacoustic TI media by first-order equation. Operto et al.(2014) proposed a new method which decompose the VTI fourth-order wave equation as the sum of a second-order elliptic-wave equation plus an anellipticity correction term.

Bounded by phase velocity error range of 1%, the VTI media conventional 9-point scheme needs 12 grid points per wavelength to simulate accurately. The conventional scheme will cause serious numerical dispersion because the computational accuracy is very bad. Chen(2012) proposed a novel idea called ADM. ADM scheme can not only suitable for equal and unequal directional sampling intervals, but also retain high precision. We extend this idea to the VTI media qP wave equation aim to improve the computational accuracy effectively. This paper firstly propose a VTI media ADM 9-point FDFDM scheme. Then we use the least-square method to solve the optimized coefficients of the VTI media ADM 9-point scheme and fulfill the dispersion analysis. The result shows that the VTI media ADM 9-point scheme can decrease the required number of grid points per wavelength from 12 to 3.57. Therefore the computational accuracy improves obviously compared to VTI media conventional 9-point scheme. Finally we construct VTI media ADM 9-point PML wave equation and the numerical example shows that the VTI media ADM 9-point FDFDM scheme can achieve high precision modeling.

Summary In this paper, we present a new optimal second order traveltime formula based on Chebyshev polynomial and simulated annealing method in homogenous and VTI media. Compare with the high order equations based on Taylor expansion, this method not only reduces the calculation amount of traveltime through lowering the order of traveling-time formula, but also achieve almost the same accuracy with the high-order ones within the limit of mid-long offset. Then, we apply this formula in bend-ray Kirchhoff pre-stack time migration (PSTM) to test its correctness and accuracy. Finally, through the method verification of homogenous media, VTI media and field data, it is proved that this modification can cost less calculated amount of traveltime to acquire a comparatively same migration profile with the high order formulas. Introduction Traveltime calculation is a key factor to Kirchhoff migration.

The finite-difference methods have been widely utilized in seismic wave numerical modelling, seismic imaging and inversion.we can truncate spatial convolutional counterpart of the pseudospectral methods to get finite-difference operators using truncated windows, and the properties of truncated windows in amplitude responses play a major role in finite-difference approximation, narrower main lobe and larger attenuation of side lobe bring higher accuracy of finite-difference approximation, we propose an optimized finite-difference operators based on Chebyshev auto-convolution combined window which has narrow main lobe and large attenuation of side lobe in its amplitude response. Through adjusting three parameters of auto-convolution combined window, visually and intuitively control the properties of main lobe and side lobe to adjust accuracy of finite-difference approximation. Numerical dispersion analysis and elastic wave numerical modelling demonstrate that our finite-difference operators have higher accuracy than the conventional finite-difference operators and can more efficiently suppress numerical dispersion under the same condition.